Corrgiendum to "From $A_1$ to $A_\infty$: new mixed inequalities for certain maximal operators''

TL;DR

This paper corrects and extends mixed inequalities for generalized maximal functions, including fractional variants, under specific conditions on Young functions, broadening the applicability of classical maximal operator estimates.

Contribution

It provides corrected estimates for mixed inequalities of the generalized maximal function and extends these results to fractional maximal operators with $L ext{-}logL$ type Young functions.

Findings

Corrected estimates for mixed inequalities of $M_ ext{ extPhi}$

Extended inequalities to fractional maximal operators $M_{ ext{ extgamma}, extPhi}$

Applicable to Young functions of $L ext{-}logL$ type

Abstract

We devote this note to correct an estimate concerning mixed inequalities for the generalized maximal function $M_\Phi$, when certain properties of the associated Young function $\Phi$ are assumed. Although the obtained estimates turn out to be slightly different, they are good extensions of mixed inequalities for the classical Hardy-Littlewood maximal functions $M_r$, with $r\geq 1$. They also allow us to obtain mixed estimates for the generalized fractional maximal operator $M_{\gamma,\Phi}$, when $0<\gamma<n$ and $\Phi$ is an $L\log L$ type function.